Related papers: Braidoids

We prove that the Alexander polynomials of certain families of alternating 4-braid knots satisfy Fox's Trapezoidal Conjecture. Moreover, we give explicit formulas for the signature and for the first 4 coefficients of the Alexander…

We describe symmetries of the braid monodromy decomposition for a class of plane curves defined over reals including the real curves with no real points and proving new divisibility relations for Alexander invariants of such curves.

Braid groups are an important and flexible tool used in several areas of science, such as Knot Theory (Alexander's theorem), Mathematical Physics (Yang-Baxter's equation) and Algebraic Geometry (monodromy invariants). In this note we will…

In this paper we will present the results of Artin--Markov on braid groups by using the Groebner--Shirshov basis. As a consequence we can reobtain the normal form of Artin--Markov--Ivanovsky as an easy corollary.

It is shown that two braids represent transversally isotopic links if and only if one can pass from one braid to another by conjugations in braid groups, positive Markov moves, and their inverses.

We show that a transverse link in a contact structure supported by an open book decomposition can be transversely braided. We also generalize Markov's theorem on when the closures of two braids represent (transversely) isotopic links.

Tied links and the tied braid monoid were introduced recently by the authors and used to define new invariants for classical links. Here, we give a version purely algebraic-combinatoric of tied links. With this new version we prove that the…

General braided counterparts of classical Clifford algebras are introduced and investigated. Braided Clifford algebras are defined as Chevalley-Kahler deformations of the corresponding braided exterior algebras. Analogs of the spinor…

In this paper we look at which Alexander and Markov theories can be defined for generalized knot theories

Given a knot or link in the form of plat closure of a braid, we describe an algorithm to obtain a braid representing the same knot or link with the standard closure, and vice-versa. We analyze the three cases of knots and links: in…

In [Jo14] and [Jo18] Vaughan Jones introduced a construction which yields oriented knots and links from elements of the oriented Thompson group $\vec{F}$. In this paper we prove, by analogy with Alexander's classical theorem establishing…

We define a new homotopy algebraic structure, that we call a braided $L_\infty$-algebra, and use it to systematically construct a new class of noncommutative field theories, that we call braided field theories. Braided field theories have…

In this paper we introduce the tied links, i.e. ordinary links provided with some ties between strands. The motivation for introducing such objects originates from a diagrammatical interpretation of the defining generators of the so-called…

Braided deformations of (symmetric) monoidal categories are related to Vassiliev theory by a direct generalization of well-known results relating "quantum" knot invariants to Vassiliev invariants. The deformation theory of braidings is…

Generalizing work of Marin [12], we construct in a unified way all the "braids and ties'' algebras available in literature and new ones.

In this paper, we introduce twisted virtual doodles, defined as stable equivalence classes of immersed circles on closed surfaces that may be non-orientable. These objects admit planar representative diagrams, considered up to a suitable…

In this paper, we define generalized braid theories in alignment with the language of Fenn and Bartholomew for knot theories, and compute a generating set for the pure generalized braid theories. Using this, we prove that every oriented…

A correspondence is studied by H. Matsuda between front projections of Legendrian links in the standard contact structure for 3-space and rectangular diagrams. In this paper, we introduce braided rectangular diagrams, and study a…

Torus knots are an important family of knots about which much is understood; invariants of torus knots often exhibit nice formulas, making them convenient and fundamental building blocks for examples in knot theory. Spiral knots, defined…

The notion of Vassiliev algebra in case of hanlebodies is developed. The analogues of the results of John Baez for links in handlebodies are proved. That means that there exists a one-to-one correspondence between the special class of…